There are two count ries, Canada (CAN) and Mexico (MEX). Consumers in both coun. tries have identical preferences over two goods, oil and corn, with utility given by; parameter S E (0, 1) indicates how much consumers like oil relative to com. We will denote relative price of oil to com. Each country is also endowed with stacks of two productive factors, capital ( K) and labor (2). which are owned by consumers. Endowments of capital and labor are: RCAN - 10 RMEX - 2, CAN - 5 LMEX - 8 We will denote the prices of capital and labor by r and a respectively (CAN, MEX) and sector i E foil, corn}. production uses the following Cobb-Douglas tech- nology: where X5. K;, and 2: denote output, capital input, and labor input respectively in sector in country c. All output is produced under perfect competition Note that the param productivity differences across both countries e and sectors i, while the parameter allows for differences in factor intensities across sectors, Below, you will consider four scenarios that differ in terms of how mobile factors are across sectors and in terms of the parameters {S, 7,. A.) of the utility and production functions. Treat each scenario independently. Each scenario has questions that are worth 30 points in total, for a grand total of 120 points. Answer all questions. Scenario 1 Both capital and labor are specific to individual sector sectors. In Canada, the allocation of factors is: be reallocated across CAN = KCAN - 4, LOAN - while in Mexico, the allocation of factors is: KNEX - 1, LNEX - LMEX = 6 Assume that Aud = dome = ] and that ZY = 1 in all countries and sectors. Assume that a) What is the relative price of oil to corn, If = Past/Pawn in each country e under autarky? (10 points) b) Which country has a comparative advantage in which sector? Explain clearly the economic reasoning behind your answer. (5 points) c) What is total consumer utility U" in each country c under free trade? (15 points) Scenario 2 Suppose that dad = doorn = 1, so that capital is not a productive factor and earns zero income. Labor is freely mobile across sectors but is immobile across countries. Productivityes TOAN TOAN = while productivityes in Mexico are: THEX - THEX - 1 Assume that S= . (a) What is total consumer utility De in each country c under autarky? (15 points) b) Suppose that under free trade, there is complete specialization, so that each country only produces in one sector. What is the world relative price of oil to corn under free trade. p. = Pla/P" ? (15 points) Scenario 3 are = . Capital is freely mobile across sectors but is irumobile across countries. Labor is specific to individual sectors and cannot be reallocated across sectors. In Canada, the allocation of labor is LOAN = while in Mexico, the allocation of labor is: LMEX - LMEX - 6 Assume that Ty = 1 in all countries and sectors. Assume that S = 1. ) What are real incomes for capital owners r'/of in each country c under aut arky? (Note: you should calculate real capital incomes in each country using goods prices in both sectors.) (20 points) would real incomes increase, decrease , or stay the same)? Explain clearly the economic reasoning behind your answer. (10 points) Scenario 4 Suppose that And = 1 and doorn = 4- Both capital and labor are freely mobile across rectors but are immobile across countries. Assume that 7? = 1 in all count ries and sectors. al Suppose that the preference parameter S is and Mexico are p= | and pyEX = v2 respectively. What is the relative price of capital to labor, rout, in each country e under anarky? (15 points) (b) Now suppose that Canada and Mexico open to free trade with each other. How would you expect the relative price of capital to labor, " fur, in each country e to change after opening to trade (Le. would the relative factor price in each country e increase, decrease, or stay the samej? Why do relative fact r incomes change in this way? Explain clearly the economic reasoning behind your answer. (10 points) relative prices in part (al" (Note: This is a hard question and is intended as a bonus. You should not attempt to solve this until you have completed all other parts of this exam.) (5 points)